Remember when you thought about measurement and fractions in the last Concept? Well, Travis is actually going to work on a construction site.

Travis is hoping to work with his Uncle Larry for the summer. Uncle Larry is a contractor who works on building houses. Travis has always loved working with his hands and construction seems to be a perfect fit for him. He also loves seeing a house start from nothing and be built. Travis’ Uncle Larry is a bit concerned because Travis is a little young to be working on a construction site, but Travis is sure that he is up to the task. To test things out first, Uncle Larry has asked Travis to come and work with him during school vacation week. He is finishing a house and there are some jobs that Travis can help him with. Travis is thrilled. He can hardly wait for the first day, and after what feels like forever, it has finally arrived.

Travis and Uncle Larry arrive at the site. They are going to be working on finishing a part of a wall. When they arrive, there are bunch of boards and tools waiting for them.

Here is the dilemma.

Two wall studs have already been nailed into the floor. Travis and Uncle Larry need to add in the brace that goes between the two studs. The space between the wall studs measures
. The board that they wish to use is
long.

“Travis, this is your first task,” Uncle Larry says. “While I go and check on some other work, I need you to do a few estimations. First, figure out if the board we have will fit. Then, figure out how much of the board we need to cut off to fit between these two wall studs. Do you have any questions?”

“Nope,” says Travis getting out a piece of paper and a pencil.

Travis knows how to figure this out, do you? Well, if you don’t, you will by the end of the Concept. This Concept is all about estimating with fractions and whole numbers. Pay close attention, we come back to solve Travis' problem later!

Guidance

We can also estimate by rounding
mixed numbers
. Remember that a mixed number is a number that has a whole number and a fraction. A mixed number refers to a number that is between one whole number and another.

How do we round mixed numbers to the nearest whole?

To do this, we need to look at both the whole number part of the mixed number and the fraction part of the mixed number. The whole will tell us which two numbers the fraction part is between.

is found between the whole numbers 5 and 6.

Our answer is 5.
is closer to 5.

In the example we just looked at, one-sixth is a very small fraction. If the fraction part of the mixed number had been one-half or greater, then we would have said that five and one-sixth was closer to six.
We can think in this way whenever we are rounding mixed numbers.

Practice by rounding these mixed numbers.

Example A

Solution:

Example B

Solution:

Example C

Solution:

Now back to the dilemma.

Two wall studs have already been nailed into the floor. Travis and Uncle Larry need to add in the brace that goes between the two studs. The space between the wall studs measures
. The board that they wish to use is
long.

“Travis, this is your first task,” Uncle Larry says. “While I go and check on some other work I need you to do a few estimations. First, figure out if the board we have will fit. Then, figure out how much of the board we need to cut off to fit between these two wall studs. Do you have any questions?”

“Nope,” says Travis getting out a piece of paper and a pencil.

The first thing to notice is that the space is being measured in inches, and the boards are being measured in feet. Let’s change the feet to inches first.

is the board length.

The space measures
.

The first thing that Uncle Larry wanted Travis to figure out was if the board would be long enough to fit the space. 54” is greater than
, so it will work, but the board will need to be cut.
To figure out how much board to cut, we need to find a difference. We can estimate the difference by rounding.

54” is already a whole number.

is closest to 44. We round it up to 44”.

.

Travis and Uncle Larry will need to cut approximately 10” from the board to have it fit into the space. Fractions and mixed numbers are used all the time in real life dilemmas like Travis’. Contractors use fractions all of the time!

Vocabulary

Here are the vocabulary words in this Concept.

Fraction

a part of a whole written with a fraction bar, a numerator and a denominator.

Estimate

to find an approximate answer that is reasonable and makes sense given the problem.

Mixed number

a number made up of a whole number and a fraction.

Sum

the answer to an addition problem.

Difference

the answer to a subtraction problem.

Guided Practice

Here is one for you to try on your own.

Sarah is helping to measure a hem on a dress. She measures that the dress needs to be shortened
inches. Given this measurement, does it make sense for Sarah to round down to 6 or up to 7 inches?

Answer
Given that
is greater than one - half, it makes sense to round up. Sarah should round up and shorten the dress by seven inches.